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Discrete approximations of strong solutions of reflecting SDEs with discontinuous coefficients

Semrau A.

Bulletin of the Polish Academy of Sciences. Mathematics

2009

Vol. 57, no 2

169-180

We study Lp convergence for the Euler scheme for stochastic differential equations reflecting on the boundary of a general convex domain D ⊆ Rd. We assume that the equation has the pathwise uniqueness property and its coefficients are measurable and continuous almost everywhere with respect to the Lebesgue measure. In the case D = [0, ∞) new sufficient conditions ensuring pathwise uniqueness for equations with possibly discontinuous coefficients are given.